071 = Snap Probability and Zombie Mobility

Hello and welcome to A Problem Squared, the podcast which is a bit like Halloween, except our listeners come to us with problems instead of wearing adorable costumes, and we provide solutions instead of candy.

We don't know what costumes our listeners are wearing.

No, but that's my point.

They're not coming to us with adorable.

Oh, that's true.

We don't see them, good Good point.

Yeah.

I mean, they can if they want.

That's true.

I'm your host, comedian, and presenter, Beck Hill.

And I'm a lot like a zombie in that I'm often lacking in brains.

Oh, that's not true.

And I'm joined by your other host, mathematician and YouTuber, Matt Parker, who is a lot like a vampire because he sucks.

Oh, my goodness.

Wow.

Yeah, as soon as you were being nice and you're like, that's not true, Beck.

I was like, oh, just wait.

Oh, mate, just you wait.

Sorry, I'm going to bring us both down.

Dang.

You're consistent.

It was either that or you're like a

the other one was you're a werewolf in that you're quite hairy in places you wouldn't expect.

That is true.

Talking about a beard.

Yep.

That's the intro

in this episode.

I do some spooky card maths.

I'm going to be thinking more about zombies.

And we have some terrifying A.

Oh,

boozeness.

Boozeness.

Boozeness.

Stay tuned.

Hello, Matt.

Hello, new listeners.

Yes.

Hello, audiences.

We don't often theme an episode around a holiday.

No, we did do a spooky episode a few years ago where

people sent us their supernatural problems.

That's it.

And I did like the pumpkin, hole in a pumpkin

solution.

And I think mine was how to get rid of a ghost.

It was like us.

So, but yeah, we haven't done one for a while.

No, I got lucky.

There's a problem that came in.

I just went, oh, that's a bit, it's a bit weird.

I was like, I'll just call it spooky.

Halloween.

Here we go.

I did threaten you.

I did say that.

You did.

You've got to make it spooky related.

Yeah.

Yeah, yeah.

Good.

I appreciate that.

You're welcome.

Have you been?

I've been all right.

I'm now acutely aware.

that we're going to blink and the year 2023 is going to be over.

It's been a fast year.

Yeah, it's been a real swift.

and yet slow i don't know about you but every now and then i think i remember something that happened you know like earlier this year yeah yeah and i'm like wait what when was that feels like it was ages ago yeah so so i'm i am also i'm going back to australia for christmas yes we fly out late november very jealous so it's gonna be great and

that just amplifies everything because i realize that's like what five six weeks away now

i'm suddenly gonna have i'm gonna be in australia so i've actually got less UK time left than I expected.

And so I do, we, we need to discuss and I need to sort out separately Christmas cards for the year.

Yes.

Because for new listeners, we do a Christmas card for our Patreon supporters.

So we will, we send out an e-card.

Yep.

We send out an e-card to our.

Everyone gets an e-card.

Everyone gets an e-card.

Patreon supporters.

Yes.

And the wizard-level supporters get a hard copy signed card we both sign a card and we send it out yeah and i and i design the card you design the card yes and i have a similar system for my uh youtube patreon supporters who support the standout maths channel but i always try and do a ridiculous maths card that ties into a video that will be coming out at about the same time so when you asked how i've been i suddenly realized i haven't got that long left to come up with an interesting maths thing that can be both a video and a card and i've got a prototype here so i actually thought i might test it on you, if that's okay.

Is this part of your problem or just part of your chat?

This is chat.

Wow.

I know.

I'm using chat to help

you.

Solve your problem.

Yeah, base.

Yes.

Yeah, cool.

You know, the podcast is problems all the way down.

We've been through.

Okay, so inside the card, there will be eight presents numbered two through nine that you can cut out.

They're like pictures of presents.

I'm putting these in front of back right now.

Yeah.

And the design will make them look a lot nicer.

I was just trying to mock them up.

And then on the front of the card is a picture of a Christmas tree.

I don't know if you want to describe that for the listeners.

Yep.

So So Matt's showing me a

stock image.

It's still got the watermark.

Yeah.

It's covered in baubles.

Correct.

And they're all numbered.

Yep.

But I have noticed that it's not consequential.

What would you say if it's just the numbers one, two, three?

Sequential.

Sequential.

There you go.

Consequential.

I was close.

They are consequential.

They are.

I pretty much for sequential, though.

I'm very excited.

You put consecutive and sequential together.

I did.

I got consequential.

Yeah.

There you go.

Also, thank you.

Twice as right for seeing me.

Which sadly this time made a wrong.

Yeah, which is not mathematical.

We need a saying for that.

Anyway.

Yeah.

So the way this works is you pick two presents.

So do you want to pick two presents?

Any of these numbers?

Yeah, because I will say that these, yeah, these numbers are,

I wouldn't be able to count them all over the place.

They're all over the place.

Yeah, I have no idea how many there are.

They are in very, they're very specific numbers and very specific heights.

Aha.

So if you take two presents and put them under the tree.

Okay.

So I'm going to take this one, which is, you've you've put it this way, so I'm guessing it's a nine.

It's a nine.

Yeah, actually, I didn't think I haven't labeled which way up.

These are things you need to write down.

I need to make a note.

Hang on, let me make a note on that.

Oh, what do you got there?

Nine is quite tall.

Nine is very tall.

Eight is little.

Okay, small.

See what?

Put them, and you've put them on.

There's a line at the bottom of the tree.

You've got them next to each other.

Stack them one on top of the other.

Oh, okay.

Yeah.

So now slide that stack along.

And the presents should sit directly underneath one number on one bauble.

Okay, yeah.

So they'll be close to other ones because there's a lot of baubles, but they are close, but it look it perfectly lines up with bauble 36 so it lines up perfectly with the number on i'm making a note i've designed it to match the number location and your instinct was to get it on the bauble yeah because so to switch to bauble right got it okay and so the number they line up with is 72 72 yeah which is nine times eight ah So if you take any two presents,

they will line up with what we would call the product if you multiply them.

So, I'm leaving the eight, yeah, Fonzos, but I'm swapping it out with a five, five and two

people at home, yep, and that is lined up perfectly with Bauble 40.

Oh, five and eight, yep, yeah, 40.

There you go, yep.

So, every single let's go for

seven and nine.

Oh, go for the big ones, yeah, they're the two.

It's gonna reach a long way up the tree, there's only one at the top, so I can only assume.

Oh, no, it doesn't reach that.

No, it reaches 63, which is 73.

But those are the two largest presents.

How would you get all the way up to 49?

Well, I'd have to add another present.

You'd have to have two sevens.

Oh.

So now, this is one downside to the card.

To square a number, you need two copies of it, which is why I did.

I printed out two sheets, but I've not cut out the other one.

Ah.

But if I was to cut out the other seven,

and if seven and seven, it would line up with 49.

Nice.

And this is a non-working that out is a non-trivial task to work out what height each one needs to be because there's some of these you can get there in more than one way so that 18 that could be a nine present and a two or it could be a six and a three wow they have to hit the same height but then the heights also have to work with every other multiple of six and of three so it's a very complicated

like

system of heights such that you can get every single product and what what would be the the real-world application of this famously charles babbage designed a mechanical computer in the 1800s, never got built.

The second person to do that was an Irish mathematician who wanted to have a way to turn multiplication into addition.

So you're adding together the heights and it's giving you, instead of giving you the sum, even though you're adding the heights together, it's giving you the multiplication of the two.

And this was designed originally to be able to mechanically do multiplication by just incrementing something across.

Like you could be rotating a cog, you could be moving a stick, like you can physically be incrementing a thing

and it turns multiplication, which is normally like a two-dimensional thing into a one-dimensional offset, which you can then automate.

Is that like how an abacus works?

It's a bit like how an abacus works.

But an abacus, you're doing addition because you're sliding extra beads across.

But it'd be if you were to.

It'd be like an abacus, but you'd get the multiple.

you'd get the product instead of the sum when you're sliding yeah now you can do multiplication on an abacus

but you're just using it to kind of keep track of what you're doing.

It's not actually doing the multiplication for you.

You don't have to do anything other than pick the two things you want to multiply

and put them next to each other.

And I had the benefit of coming up with this.

This is my set of numbers, but I was able to use a computer to find them.

Whereas

the original, this was done to invent the computer.

So the original time this was done, they didn't have the advantage of the computer.

So I found far more efficient ways of doing it, which is why I was able to turn it into a Christmas.

Thanks to technology.

Thanks to technology.

But before it was done using brain power.

That you had to sit down and try and find sizes of presence in my context that would work, whereas I just wrote some code to find the best possible size.

But that's the difference between you and me is if...

if we both had to come up with this thing, you'd write some code and I would sit there and just put things on top of each other and work out the long way about how to do it.

Which is how it had to be done originally.

Yeah, but that's my style of it.

I like to know how it's all done because

I can't fathom it otherwise.

So, anyway, I had a lot of fun with that, but I've been doing it for so long, and it's kind of so close to me, I've lost track of how it would work.

But I found two very useful bits of feedback from you trying it.

Thanks.

That's really nice.

Very useful.

And that, Beck, is how I've been doing it.

Well, I just want everyone to know who's already a Patreon supporter or considering becoming a Patreon supporter that

my design won't be this.

No, no, no.

This is for the mass Patreon people.

Beck would do a much more important thing.

I haven't thought about it yet.

Look, it might be interactive and creative.

I haven't even thought about it yet.

It's also a ton of reminder, if people want to support us on Patreon just to get the Christmas card.

That's fine.

Yeah, yeah, you can stop afterwards.

Everyone who's supporting us at the end of November.

So you've got to get on board.

So on the 1st of December, all everyone who's a supporter at the wizard level will get posted a card and everyone will get emailed a card.

Yes.

How are you doing, Bec?

I'm doing very well.

As of this episode coming out,

in two, in a week and a bit, just less than a week.

A week in the Smidge, I'm going to be hosting Brussels Comic-Con again.

Oh, again.

Yeah, they're doing two.

Oh, is that another one?

Yeah, because May was the last one.

I honestly thought I've lost all sense of time passing.

I know.

I keep getting confused because I'm like, wait, wasn't I?

And I'm like, yeah, no, I've already done one this year.

That's why I feel confused.

The lineup is absolutely off the charts.

I mentioned this before we started recording.

I did.

But the biggest guest so far is

Jean-Claude Van Damme, which I'm going to have to pronounce better.

You better practice that.

He's the Mussels from Brussels and we'll be in actual Brussels.

What?

So I think we might be interviewing because we host the main stage, Matt Hyton and I.

So I imagine if he's doing an interview, it'll be on our stage.

You get to interview him.

Yeah.

But also, there's a couple of times that we've had Belgian guests.

And so we, the interview is conducted in English because all the, everyone at Comic Con can speak English.

But what will happen is then when we go to the audience, we'll get quite a few people asking questions in French or French or, you know, English.

Chevron.

The mix.

Yep.

And

so then what happens is the guest will respond and Matt and I sit there like, we have no idea what's going on.

We can't, we don't know if they've asked a question that's offensive or.

So what I'm saying is, if you want to ask an offensive question and you can speak.

Do it in Flemish.

Yeah, yeah.

But no, I'm very excited about that.

And it's

happening on the weekend of my birthday.

So it's very possible that I will be interviewing Jean-Claude Van Damme on my birthday.

Wow.

She's very excited.

But you know who else I'm excited about?

Now, UK listeners might not be, and some European, I don't know, I don't think it had as big a reach here as it did, definitely did in America, but in Australia, you know who one of the other guests is.

I can't believe you've opened with John Claude Van Damme, MacGyver,

Richard Dean Anderson, who's also in Stargate.

I think Stargate.

That's a big thing, but like, I was a huge MacGyver fan as a kid.

Like, I mean, I don't.

Can you tell that I was somewhat influenced by MacGyver?

I think you've MacGyver's several things

today.

Yeah,

so yeah, that's

that I'm

very, very excited.

But also, we've got James Masters, James Masters, Okay.

Spike from Buffy.

Oh, my goodness.

And the spin-off series Angel.

I know.

Very excited.

Robert Patrick.

What is this?

Who's the second Terminator?

Very late 90s.

I mean, yeah, it's all the big hits.

I mean, yes, a lot of people will be excited about this.

Jenna Coleman, who was one of the companions in Doctor Who.

Okay, I'm going to need the name of the actor, Colin, what they did.

Yeah.

Oh, that's what I've been doing.

Yeah, yeah.

But you leave a beat to see if I have a flicker of recognition on my face.

Joseph Marcel, who played the butler in Fresh prince of bolair see that's how you do it yeah jack gleason who's joffrey in game of thrones oh i haven't seen it so for me

matt has thank you that's why matt and i host together

between us you've seen it all we've seen the stuff yeah there's a lot of incredible uh incredible guests and there's like as of the time of recording there's i think still five or six guests left to be announced oh my goodness which means when this comes out there'll be even more guests there'll be even more guests i'm very excited can people still get tickets to go to brussels comic-con Yes.

Oh.

Yeah, they can.

Well, they can't because they can use their money to subscribe to our Patreon.

Ticket the Christmas card.

Some people do both.

Yeah.

Both.

Yeah.

Shout out to Chris Brandon, Denver, who's one who I've talked about before.

I showed up and the first thing he said was, this is your card.

Yeah.

Well played.

Yeah.

Everyone who's going to Comic-Con, ask Bec if this is her card.

Yeah.

So that I realize that that's not me saying what I've been up to.

Well, you've been anticipating it.

But I am looking forward to it.

And do you know what?

I thought I'll mention it now because there might be people that want to go.

Go along, they can say hi.

We've got listeners in Brussels.

I don't think I've gone anywhere and done a show for a while without a listener showing up.

Yeah.

That reminds me, a listener came to a talk I did in North Carolina.

Oh, yeah.

And they brought a gift that I left at home.

Oh.

I will give it to you after the recording.

Because you mentioned this in a previous episode.

Yeah.

Tell you what.

The post-credit sequence on this video.

This audio, this podcast.

The post-credit sequence on this audio content

will not be you guessing how many dice are in the jar.

Oh.

But we'll record at home, just on my phone.

The gift.

Me responding to the gift.

Yeah.

Okay.

Deal.

And then next episode, back to the dice.

Nice.

Our first problem is the spooky problem.

Our first spook problem.

Look, the problem itself is not that innately spooky, so I've really got to dial up the dressing.

Okay.

So it's for you, Matt.

It's from Maddie.

Maddie.

Who

sent this into the problem posing page?

At a problemsquared.com.

That's the one.

And they said, dear Beck and Matt, love the podcast and have a hopefully interesting problem for you.

Thank you for saying you love the podcast, by the way.

Imagine if you started out, hate the podcast, but here's a problem.

You're my last resort.

I want to punish you.

It's a terrible problem.

They said, The scene, a mathematical problem posed by a colleague being discussed in the staff room.

I like this.

I think all problems should be sent as scripts.

There should be like, oh, yeah, opening shot, exterior.

Yeah.

Karen, 46, short hair.

That's how they describe them in scripts.

Yeah, yeah, yeah, yeah.

G'day, Karen, if you're listening.

The problem:

two people playing snap.

Is the probability of getting snap?

I think maybe we do playing snap in the card game.

Is the probability of getting snap the same or different if played with two whole packs of cards?

They put in brackets 52.

Yeah, just yeah.

In case they were using scorpor cards, which is 40.

Ah.

So they said our thoughts,

just in case you want a little

flavor.

Our initial thoughts were the probabilities had to be the same for both, but started doubting ourselves after some crude mental calculations.

I like the, for me, crude mental calculations is 60 now under.

None of us were completely convinced one way or the other.

Then the bell went for chew to time.

I mean, there has to be a school.

It's got to be a school.

Then the bell went for chew to time, so we haven't found the answer.

Our plea.

It's driving a few of us crazy.

So please, could you do the maths to show what the probabilities would be in each case and therefore whether they are the same or different?

Thank you so much.

Binge listened to this podcast over the summer and sad that I now have to wait two weeks for new episodes.

No, you should have been here in the one release.

I mean, they did have to wait three weeks for the last one.

Three weeks for the last one, one week for this one.

There you are.

Yeah, or one week.

One week.

I've stuffed that up already.

There you go.

So, so I'm going to recap the problem.

And I have brought cards.

I know they're not great props for the radio, but bear with me.

And you've got the classic bicycle standard cards, which magicians tend to.

I do.

And I just realized that I haven't used these cards before.

I thought they were a used pack.

You know, if you'd done this with tarot cards, you could have made it a spooky Halloween one.

Ah, that's true.

But instead, you've done zero effort to make this

through the power of audio only.

Now they are tarot cards.

So you've hang on them.

And

I don't know if we've got that

Foley work.

Hang on, hang on.

Matt just tried to do some fancy shuffling.

And they're brand new and they're almost.

Yeah, you're blaming the cards.

I'm going to use the phrase stiffer than I'm used to.

We're all going to be adults about it.

A magician,

a bad magician always blames the cards.

Yeah, sorry.

Let me just warm these up.

Oh, there we go.

Imagine that Matt is doing some incredible shuffling.

If he was doing this at a table, you'd be like, this guy's cheating.

It's card shop.

So,

one deck of cards.

Did you say card shop?

Sharp.

Sharp.

Sharp.

What's a card sharp?

It's like a card shark, but pointier.

Oh, okay.

I think sharp's the original phrase.

A card sharp.

Card sharp.

Yeah, what's the point?

I imagine it's like a lone shark.

I can't stop playing as a card shark.

Oh, yeah, because otherwise you die.

So while that's happening, I've got two more decks of cards.

So you've got three decks out now.

I've now got three decks out.

Okay, so

on Beck's right,

I have a single deck of cards I've just shuffled expertly.

Here, I now have a double deck of cards.

I've put two decks of cards together and I'm shuffling them together.

Yes.

So the question that's been posed by Maddie is, if we're playing snap with the single deck of cards,

is that any different to playing with a double deck of cards?

Okay, so there's a deck of cards.

I want to get your initial impression.

In fact, listeners.

Don't start working it out.

I just want to know everyone's initial impression.

So on one side, you've got a regular deck of shuffled cards.

On the other side, you've got two decks shuffled together.

And we're going to play Snap.

Okay.

Does that make a difference to the game?

And I've simplified this down to like a single kind of snap event, which is where I'm going to turn over one card to start with.

How does snap remind me of the rules of snap?

Oh, they vary.

Because I think that makes a difference.

They do vary, but at its heart...

you're turning over a card and you're saying snap if it matches

but sometimes you'll have multiple piles or one pile or,

yep.

Yeah, okay, yeah.

So what I've done, and sometimes you turn them simultaneously, sometimes people take turns turning them over.

So what I've done is I've just reduced it down to the turning event.

You've got a card already out.

You're turning another card.

Do they match or not?

Because I feel like when I used to play it,

you would deal the cards

evenly.

So both...

people would end up with half the deck or something,

yeah.

And then you would both at the same time put out your cards.

And if those two match, then you have snap.

But that is then different, isn't it?

Because it means you can't snap to the previous card or the card after it.

It has to be the card that lines up with it.

Yeah, but mathematically, there's one card and another card if it matches or not.

So

I'm pretty confident, and people correct me if I'm wrong.

I'm sure people will write in if I am, that almost all versions of snap can be reduced down to do two cards match or not.

Okay, yeah.

And I'm doing it slowly so we can think about it easily by saying there's the first card as a six yeah and we're just doing it on numbers just on numbers yeah otherwise there would be no match we can't do it on numbers

you could do it numbers and colors you could do numbers and colors correct but again you could read the same logic would apply to numbers and colors okay i'm just doing numbers there's a six the question is when i turn the next card over what's the probability there being a snap and so i turn it over

for the hell of it here we go turn it over It's a seven.

No snap.

Okay.

But what if we did that with two decks of cards?

I'm also going to point out that it's it's a different suit.

It is different.

So they know

that Matt has shuffled them properly.

Okay, that's a nine.

So that's from the double pack.

And I'm going to turn over the...

What's the probability the next card's going to match?

Turn it over.

Ah, snap.

Snap.

That was an accident.

Yeah.

Wow.

And that actually happened.

That's not just through the magic of audio only.

No.

That happened live in the room.

So what's your initial impression?

Is it the same game playing with two decks shuffled together?

Or is it a different game because the probabilities will be different?

I...

My initial thought.

And just the context, a room full of math teachers.

I know I'm assuming they're maths teachers by the context.

I mean, they'd asked you to do the maths, so.

But probability is famously difficult.

And our intuition as a human is terrible at probability.

That's true.

So this is why there's no right or wrong answer here because they couldn't decide.

And I will reveal what my initial impression was in a moment.

People at home.

Decide yours, people driving as well.

Beck, what would you say?

My initial

thought is that it's the probability is the same.

If you could hear that, that is...

My dog falling off the sofa.

Dog falling off the sofa.

Okay,

she's okay.

We really need to start filming these sessions

or not.

My initial thought is that the probability is the same because while you've got more cards that are correct, you've also got more cards that won't be correct.

Yeah, the same cards.

I thought they should be the same.

Like, if I had one short straw and 49 long straws,

the chances of you pulling out the short straw are one in 50.

Correct.

If I had two short straws

and 98 long ones, they're still one in 50.

You're two from 100.

One and 50.

Yeah.

Yeah, I do it like as if.

You're 100% spot on.

Yeah.

It's not the same.

Huh.

They're different.

Spooky.

There you go.

So, and what I find particularly weird is I've got the whole double deck here.

I could have then shuffled two together.

Got some big deck energy happening there.

I got big deck energy.

And I could have taken half off down to a regular deck size again.

And so now it's still a different game.

Because I shuffled two decks together and then took half.

The probability on this side is different.

Because you might end up with loads more of the same card.

in

one half due to the shuffling.

It doesn't make a difference on average because as often you will have fewer.

Right.

So actually that all averages out.

Okay.

It's not because, and you're right, because depending on where they clump,

the actual ability is different because if you knew what the cards are, obviously they might all be at the bottom, might all be at the top, it could be in this half or that half.

But if we don't know,

it's all equal.

This could be any of the remaining, in this case, 103 cards.

before you turn it over.

Yep.

And so I was like, that's interesting.

And I can see why they got into an argument because it feels like it should be the same.

But then obviously they had an inkling that it wasn't.

And so I wrote some terrible Python code to

snap.

That eventually is going to be some merch, isn't it?

Yeah, yeah, yeah.

And so I wrote some terrible Python code.

If we do a live, if we ever do a live tour of a problem squared, that's going to be a call and response thing.

And so I wrote some terrible Python code.

Everybody drink.

So I, so I did.

And I wrote it to play Snap this version and keep track of the probabilities as it goes.

Yep.

So I can tell you the actual probabilities.

So if you've got a single deck and you put the first card out the probability of another card matching with it is 5.88%.

Okay.

If you've got the two decks the probability of two cards matching is more than 5.88%.

It's 6.8%.

Why?

It's more likely.

Why?

That's a great question.

Why?

Why would that be?

So I wrote the code to play snap with progressively more and more suits of cards.

So it started with a half deck, only two suits.

So you can see if they match or not.

And then it started with a deck with three suits and then four suits and then five and then all the way up.

And so along the way, it did a whole deck and two decks and everything else.

And the matching rate increases as the deck gets bigger until it approaches a one in 13 chance.

Which makes sense because if you had infinitely many cards and let's say you want a six one out of every 13 cards is a six because there's 13 cards in a suit.

And then you're like, well, hang on, well, why isn't that the case here?

And it's because

Matt is pointing at the single deck or either of these

in a finite deck.

Yes.

It's because that first six, once you turn it over, the remaining 12 cards from its suit are getting in the way.

And they're diluting the chance of getting another matching one.

Oh.

It's a little bit like the Monty Hall problem.

A little bit.

In that it's confusing probability.

Yes.

Yeah, it's nothing like the Monty Hall problem.

But in that it makes me go, oh, oh, yeah, yeah, yeah.

And for me, it was that real.

Something I went, it's the other 12 cards getting in the way.

Yeah, you can't match with those.

So now

it's making it harder to get the matching card.

It's one in 13 chance.

Plus, diluted a bit because of those 12 cards.

And when you got the double deck,

the extra 12 cards have a smaller effect because

they can blend in across a much bigger deck.

Does that mean there's only six cards in the way?

Per deck, yes.

Yeah.

So they make less of an impact on average.

Yeah.

And the more decks you're playing with, the more those more space for those 12 cards to hide until you've got an infinitely big deck and then they don't make any difference at all and you're back to exactly a 1 in 13 chance.

So what's the minimum size deck you would need for it to be oh for it to be close enough

i'd have to run the numbers it's i've made a little plot here so there's my little plot of the probability approaching one in 13

but not quite but once i realized what it was once i had the logic behind it i don't need to run the code anymore because i i played um 100 million games per

size of deck and then took the average match to get this.

But then once I I did that, I was like, well, hang on a second.

I could have worked that out because

I flipped that first card over.

The next card has a three

because there's three sixes left

out of 51 chance of matching.

Because there's 51 cards because I'll have to turn one over.

Yeah.

And on the double deck, it's a seven

in 103 chance.

And that

is a bigger fraction.

Yeah.

It's more likely to happen.

And that gives me exactly the same percentage as I said a moment ago that I got from the code.

I could have just thought, if I'd spent a moment thinking about it.

Yeah.

I could have worked that out.

Of course.

Yeah.

Yeah.

So what if you've got a pack made of 14 decks?

Because you'll have 14 times 52 minus one.

Yeah.

That'll be the total number of cards left.

And you're going to have 14 times four minus one that will match.

So

it doesn't work that way, does it?

Is it?

Oh, no, no, no.

still the same problem no no no no no no it it you can see where my brain was going

yeah your brain is trying to think is there like a point at which you've covered all the bases and it works because you've got enough that you've done everything but in this case it just gets closer and closer but never quite yeah yeah because you're still those actual cards are still in there yeah you're just they're they've got more and more places to hide as you have a bigger and bigger deck yeah so they have less of an impact on any

and i see now why it's spooky it's spooky because it's 13.

yeah there you are i hadn't thought of that don't tell me you want

it it turns out it is unlucky 13.

spooky yeah wow i'm more on brand than i expected yeah but that proved me because my instinct was wrong we all have the same instinct humans and a bunch of teachers argued about it But also, what I love about probability is my instinct is write some terrible Python code, simulate it.

But then I get the answer and I'm like, oh, that male makes, I can kind kind of reverse engineer the logic.

Yeah.

But once I realize it's those 12 cards getting in the way, I was like, got it.

See, Matt, this is my favorite kind of problem that you do because I come away from it like, that's really interesting.

Oh, good.

I end up telling other people about it.

They won't listen to the podcast still, but I'll tell them.

Oh, well, tell them about it.

We have one last bit of business on this.

Yeah.

Producer Lauren, is it card sharp or card shark?

Sharp came before shark.

Wow.

What's the etymology?

The original sharp.

oh i see yeah so apparently the root word originated in europe taken from the german word sharpen what which translates to sharpen in english and means swindler swindler a sharp swindler shafen card swindler card swindler matt i think that deserves a ding oh thanks but i feel like we need to hear from the teachers no i want my working out mark yeah yeah yeah and i'm not gonna mark it no

yeah uh teachers teachers love extra marking yeah they do.

Let us know.

Is that a ding?

Up next in our spooky Halloween, a problem squared episode.

We have a problem for Beck sent in by Jenny on the problem posing page.

And oh, Beck, your problems is on theme as mine.

That's impressive.

Arguably more.

I don't know.

Just because yours is about zombies.

So, Jenny's problem is: can zombies ride bikes?

I hope it's not a practical, a pressing practical problem.

Yeah, you can imagine if.

Oh, no, they've got bikes.

Is this going to be an issue?

Jenny's seen some zombies near a bike shop.

Get on the problem posing page.

She's got several sub-questions surrounding this problem.

Great.

Now,

I guess this is getting into the details.

Jenny wants to know, specifically, can they bend their knees?

As in, like, if they can't ride bikes, can they canoe?

Yeah.

Do they have enough energy to pedal?

Would they be able to get their leg over if it wasn't a step-through frame?

So, there you go.

So, if you're worried about zombie, you know, apocalypse,

get a bike with a top bar.

And they can't.

Because the zombie can't nicker and cycle.

You wouldn't have to lock it up.

No,

they'd bounce right off it.

So, they're thinking, so Jenny's discussed this with her friends, that the answer will depend if you consider the traditional film version of zombies with all their slow walking or the modern day, modern day fast running variation yeah what does Jenny know well you know like 28 days later I think was the the fast zombies where I remember they that's the first one I remember with fast zombies okay so they it would depend on this the uh additional model of zombie yes

I

thought this was an interesting one because yeah there are very very different types of zombies and so my my first step was to see if I could find any reference to zombies riding bikes in media.

Yeah.

Media.

And I couldn't.

No.

Now,

as we know from my Autobahn

thing, I'm not always correct.

And so someone might be like, actually, I think you'll find...

I've been reading this Victorian era novel.

Yeah.

Yeah, sure.

This is, this is, there was a zombie riding a bike.

But all I could find was there was a, all I could find was there was a zombie bike ride, you know, like a flash mob type thing, you know.

Because there used to be zombie shuffles in Melbourne once a year.

They would do the zombie shuffle.

Mid-2000s.

very mid-2000s very mid-2000s and so you'd have hundreds of people meeting up on one corner of the city and they're all shuffling and you would shuffle through diagonally to the other corner of the city at the same yeah as zombies just for fun why not yeah it was the mid-2000s yeah though i remember there being a a ninja one as well there was a fellow i knew who was part of like a parkour group at adelaide and they had a ninja ninja their way across where they ninja but they're all parkour people so dressed ninjas and stuff yeah

and i ended up using them in a video for my first solo show

because I was like, hey, can I borrow them for like 20 minutes?

And he was like, yeah.

And so there's a scene where I get chased by like a hundred ninjas because I just happened to get it in on the right time.

I'm going way off subject, though.

So

bicycles.

Bicycles.

So there, you know, there's a zombie bike ride where there are people dressed as zombies riding bicycles, but they're not actual zombies.

Not real zombies.

But I couldn't find any reference to zombies riding bikes.

So I thought I will reach out to some people who I know

who might know more about this.

So I'm wondering, bike experts or zombie experts?

Zombie experts.

Of course, it was bike experts.

I come to you, Matt.

Wow.

You're the first person I'd ask.

Funnily enough, I thought I'll start at the most,

I think at the moment,

if you Google zombie, annoyingly, the most sort of popular type of zombie is Minecraft.

Of course.

Yeah, because there's zombies in Minecraft.

So I reached out to Peter Sutton from Fox Dog Studios,

who is a huge Minecraft nerd, got really into it during lockdown and can now answer pretty much any question about Minecraft.

Including the zombie one.

So I reached out.

I said,

are there any zombies riding bikes in Minecraft?

Or

could they?

Are there bikes in Minecraft?

Do they do it?

No.

Well, I don't think so.

I don't think so.

I said, can the zombies in Minecraft ride bicycles?

And Peter said, sort of.

Sort of.

Now, I think this is made all the funnier when they continue.

Baby zombies can spawn riding chickens.

Now, I would argue that that that is not sort of like riding a bike.

But I feel like if you can ride a chicken, you can ride a bike.

No, no, I disagree.

Really?

Because

riding an animal,

you have to sit on it.

You hold it.

But a bike involves sitting and coordination.

I feel like the balance required to stay on a chicken.

No, but hand and eye coordination, as in your legs, you have to know to pump the legs on the pedals.

There's a reason that people can't just ride bikes.

I get that for free.

Like, people have to learn how to ride.

The balance is the issue.

No, you need to be able to pedal as well i don't think riding the bike is the same as riding a chicken matt and i don't i don't think i'm like everyone i don't think i'm ruffling any feathers vote below was this going to be a twitter poll twitter poll is riding a bike like riding

no no no if you can ride a chicken does that mean you can also ride a bike yeah

Please show your working out.

Apparently, the baby zombies that are spawned riding chickens in Minecraft are known as chicken jockeys.

They could have called them Jock Chicken.

Come on.

But Peter also says despite their name, the zombie has no control of the chicken.

See, it's a skilled activity.

And so the chicken often walks into one, into one high gap and kills the zombie.

That's good to know.

Yeah.

Practical information.

Yeah.

So essentially, no,

the zombies in Minecraft can't

ride bikes.

Can't ride bikes.

You know, my favorite moments when we record this podcast is we will have this discussion and we're like, right, vote.

Is riding a chicken

riding yeah.

And I can just hear a sigh and then typing in the corner.

Which is lower and

now I have to remember to make a poll.

It's a good poll.

It's funny if we don't make the poll.

I think it's an do you know what I love about this poll is I really hope that our listeners retweet it because void of all context.

Without any context.

And I don't want any context on

that question.

Make a note.

She's writing that down.

She's deleting a bunch of context.

I want there to be just

people being like, why would you ask this question?

Or Minecraft people would be like, that's true.

It reminds me of those

chicken jockeys.

So I did say, so they would probably struggle with peddling.

And Peter said, almost certainly.

There's nothing in the law that implies any sort of wheels or chain drive vehicles have even existed.

Okay.

So that was my first border call.

So I was like, right, Minecraft zombies out.

So then I was like, what about like classic horror?

Yep.

And so I reached out to Stephen Kostansky, who is a director and writer.

Excellent.

Canadian director and writer, who wrote a film that I'm going to make you watch tonight.

Oh, is that?

Oh, really?

And directed a film as well.

Yeah, it's called Psycho Gorman.

Oh, my goodness.

Matt Hyton, the other Matt I work with.

The other Matt, you know a lot of Matt.

Put me onto it.

Right.

And it is an incredible film.

So for this is, we're recording in Godaming this time, and they're where I live.

And so we're going to have a little film night.

Yeah.

Now, it's not a zombie film, but there is some reanimation that sort of goes on, kind of.

And so I was like, do you know what?

I reckon Stephen's got a pretty good grasp of classic horror.

So I reached out and Stephen replied.

Excellent.

And I said, in your professional opinion, would a zombie be able to ride a bike?

And Stephen said, I think if the zombie had a history of bike riding when they were alive, then they might be able to.

Like they were a professional cyclist or something.

Yep.

But I don't know if you could teach a zombie to ride a bike.

That's a good take.

It'd need to be something they could do purely by instinct.

So when in the classic zombification process in media,

they retain some muscle memory ability.

Exactly.

Yeah.

Because they can walk.

They can walk.

And when we're born, we can't walk.

You've got to learn.

That's a learned skill.

So, and in some cases, you see zombies sort of vaguely doing

things that they did.

And

there might be some

repetitive tasks.

Yeah.

Yeah.

I did say I love this theory.

Thank you.

And they said, happy to field any more questions like that.

That's excellent.

Our collection of experts grows ever bigger.

They said, I think a zombie rides a horse in survival of the dead.

And then they said, that's kind of like a bike.

Yeah, see, a bike is between a chicken and a horse.

I did say, I mean, what are horses if not fleshy BMXs?

Yeah.

So

that was the answer from Stephen.

Yep.

Potentially.

Yeah.

I'm getting more and more convinced.

And then I thought, do you know what?

I need at least one more.

One more, one more opinion.

So I reached out.

I sent into the the DMs of someone who I only sign into the DMs of occasionally because I don't want to overstep my.

Okay.

Don't want to.

Oh, is this like a contact where you kind of feel like you've only got so many asks per year?

Yeah.

So I asked Edgar Wright the same question.

Oh, that's amazing.

Oh, well done.

Good use of an Edgar Wright ask.

Yeah, yeah.

You're never going to get a better moment to deploy it.

In your genie free wishes thing.

and I've used one to ask this question.

Now, hope you're happy, Jenny.

For listeners unfamiliar,

this moment might be useful.

At the beginning, when they mentioned zombies riding bikes, I just imagined Sean of the Dead.

Like, that's yeah, because there's some, I think there's one where someone's like doing something in the supermarket or something like that.

And of course, at the end, Nick Frost is playing a video game.

Yep.

Pauly.

Pauly.

Oh, yeah.

Sorry.

Spoiler all that.

Yeah.

So, yeah, I asked the same question.

In your professional opinion, could a zombie ride a bicycle?

And Edgar Wright says, muscle memory, perhaps.

Oh.

So like you said, yeah.

And so I said, so do you think if they turned into a zombie while riding the bike,

they might just keep pedaling automatically.

Yeah.

And they said, I think so.

That's pretty definitive.

Yeah.

So a zombie could potentially ride a bike should the conditions be correct.

Right.

They would need to already know how to ride a bike.

Yeah.

And potentially already be on the bike.

Yeah.

That's amazing, Beck.

I don't think there's a more definitive answer possible than asking Edgar Wright.

Thank you.

I feel like you've won the Problem Squared 2023 Research Award.

So I would say the answer is yes.

A zombie potentially could ride a bike.

Potentially could ride a bike.

I think they can bend their knees to answer the sub questions.

Do they have enough energy to pedal?

I would say the same amount of energy that they have to move.

Zombies can go upstairs, right?

Ah, this was a whole thing that I found.

Oh, really?

So, uh, I didn't realize what I was stumbling into.

People were saying they can probably they can go upstairs again, if it seems like a sort of automatic, like the same as walking type thing, but ladders, probably not.

Oh, that's interesting.

Yeah.

Okay.

I was just saying, from a knee-bending point of view, yes, you can go upstairs.

Yeah, exactly.

And also, when you talk about the fast-running zombies,

then they have to bend their knees.

Have you tried running fast without bending your knees?

I look like it's hilarious.

I look like an egg beater.

Yeah, my brother and I used to to have races like that.

It was very funny.

Yeah.

Love to do in Adelaide.

Yeah.

Again, would they be able to get their logo over?

I don't know if a zombie would walk over to a bike and get on it.

Yeah.

I think they would sort of already have to be on the bike.

On a bike.

But if you put a zombie on a bike,

if they fell onto the bike.

And they previously knew how to ride a bike.

Yeah.

And you gave them a push.

Yeah.

Yes.

So.

Because, like some serious cyclists, which I think this would require,

your feet are clipped into the pedals like you're attached and so if you were zombified with your

pleats locked in yeah you just keep going so i i think i'm with jenny i think it does depend on the type of zombie yep i think one of those slow moving there's a minimum speed to keep a bike yeah upright yeah yeah so they probably wouldn't have the energy but i think some of the faster ones would less the zombie knew how to track stand

What one final piece of advice, though, is a lot of people have pointed out that if you wanted to get away from zombies, bikes would be the way.

That's the winner.

Yeah, because they don't need fuel, which a lot of people run out of.

Yep.

It's silent.

Silent.

So you're not going to.

You see in zombie films, everyone tries to drive down the nearest highway.

That gets cluttered with congestion and cars and crashes.

Bicycle, you can just weave it.

Get around, pick it up, carry it over.

Yeah.

So I think bicycles are the winner and they're less likely to be stolen.

Bicycles.

Easier to find a zombie.

If they're going to keep going, the zombie can't take it.

And they probably won't chase after you unless they're already on the bike.

So yeah, there's your answer.

Beck,

obviously, we'll go back to Jenny to get the official, but I'm prepared to give you a ding.

Thank you.

Thank you.

First bit of any other business is that we had some commemorative plates slash bowls.

Yep.

Bowls, slash plates.

Yeah.

That

people could order.

When we had a million downloads, very exciting.

Yes.

And we also sent them out to our wizard Patreon supporters.

We did.

As a nice little bonus.

Say thanks.

People in Germany,

not everyone is getting their stuff.

Not getting their plates or bowls.

This is not an us-specific problem.

No, industry-wide.

It is industry-wide.

Sending anything international.

We've done all the right things.

All the right things.

Oh, if you're thinking, but you didn't put that barcode on it, we did.

We've got all the barcodes, all the numbers, all the codes, all the categorizations, the CN22s, the works yeah

we've got everything now

i think it's because

i mean basically people in germany are sending back anything that they can find even the slightest fault with even when there's no fault and i think the fact that it's an ambiguous plate or bowl

and they're like well you can't import something that's of unknown type

and so they're sending it back Yeah, that's my theory.

Sure.

Is it a plate or a bowl?

Nah, send it back.

Yeah, let's say say that work it out then send it in that's i don't think we put that on the forms i think we just post them yeah yeah so anyway my point is is that uh if you are a wizard level patreon supporter who didn't receive it we're sorry we're very sorry we've we've tried we've tried resending them it's not happening um move

yes or if you paid money for one if you pre-ordered one very kindly we've refunded everyone we couldn't get the the plate slash bowl to yeah yeah if you're a pay, if you're a German Patreon supporter who didn't receive your

free plate/slash bowl as a surprise gift, then uh

we're sorry you found out this way, yeah, because you wouldn't have known,

or they might have been too polite, not wanting to reflect on it,

yeah.

But we'll make it up to you some way, some someday, somehow, somewhere.

We'll find a way, yeah.

Also, in a little bit of any other business, there's just a quick question from someone on the problem-posing page: nip

nibbler, Nibble.

Nibble?

Night nibble.

N-Y-B-B-L-E

says, do you use a cryptographically secure random number generator for picking the three Patreon supporters at the end of each episode?

So each episode, we thank three Patreon supporters at random, not by posting them a bowl, but just by saying their names.

And I pick them at random using an Excel spreadsheet.

There's a built-in random function.

There's a built-in random number generator in Excel, which is not cryptographically secure that I use to pick those three people.

So the answer is I don't.

I don't.

It's not.

It's not truly random.

It's pseudo-random.

Yeah.

And I apologize for not being clearer about that.

And for anyone curious, random numbers are an important part of keeping online information secure.

But if there's any patterns to those random numbers, if they could be any way predicted or understood, that could be used as a way to break encryption.

And so if you want to go all out, you can buy quantum random number generators as like a USB device that use quantum uncertainty inside the device,

photons probably, to then generate proper apps.

It's like rolling millions of tiny quantum dice.

Proper randomness.

Whereas Excel uses a pseudo-random number generator, but they're not actually random, but they're random-ish enough.

Does that mean that someone could hack it?

Someone could hack it.

Well, if we start, I mean, we have thanked at least one Patreon supporter twice.

Ah.

So if we start thanking the same person again and again and again, then we know

we need to invest in a better random number, a better source of randomness.

Which reminds me.

And what I have learned from the cards thing is that the more Patreon supporters we get.

That's a great segue.

The better the randomness.

If only we had more Patreon.

But also the lesser chance that people will get.

Individually, yes.

I mean, maybe one day we have to increase from three yeah maybe we should do that maybe if we hit in a certain number we will thank more people per episode and without any further ado we should thank we should thank three thank three people yeah so this episode we would like to thank and tony carta

i just split it up into smaller syllables

We should say it did start off as a joke that occasionally we couldn't pronounce someone's name.

And so to make no one feel left out, like a fair, we will now try and mispronounce everybody's name, like I did for Anton Y Carter, Nicholas Owens.

Ah, nailed it, no second take.

Nicholas Owens

and you Schwartz,

you, you,

we

Schwartz

squats.

That works.

I do realize this has been a very heavy mentioning the Patreon.

That's true.

But they do make this enterprise possible.

Yes.

Yeah.

We actually cannot, we can't afford to have this show edited, produced, or put out without you.

So

thank you very much.

We really appreciate it.

Of course, we thank everybody for listening.

regardless of your ability to support us.

No pressure.

And if you want to be able to help us out, but you're unable to support us on Patreon, hey, just tell someone to listen to the show.

Word of mouth is the scarce resource in the podcast business.

Whatever you want.

Get it out there.

Get it out there.

We appreciate that.

And don't forget, if you support us on Patreon, no matter what level you support us on, you automatically get access to our bonus podcast.

Yes.

I'm a Wizard.

Not just the Christmas card.

Yeah, not just a Christmas card.

You get an episode every month.

Imagine this.

Less slick.

Less professional.

Imagine this show, but without the problems that we're solving.

Yeah, yeah.

It's just the packaging.

Yeah.

More magic.

It's very magic.

I also want to thank my co-host, Matt Parker.

Spooky Matt.

Spooky.

Matt, we should do the Simpsons names.

We should.

Matt Ark!

Paark!

I'm just going to do that.

Matt!

Paarker!

I'm going to thank myself.

Beck chills chills down the spine.

Oh, well done.

Thank you.

And finally, our wonderful and patient producer, Lauren.

Oh,

strong.

Said it with more vowels.

That's all I'm doing.

Okay, it's now 10 o'clock at night.

Trousers back on.

It's funny because I'm wearing my trucky decks now.

So, we're about to watch our film.

Yeah.

And the gift that a very kind couple in North Carolina gave me is underneath this cloth.

Would you like to unveil it?

Yeah.

I'm worried something's going to jump out of it.

No, it's perfectly benign.

Oh,

it's the illicit

as to unyet untasted trader joe's baked cheese crunchies oh because this is like this is the one they're like the wenzel's ones the one we didn't get the wannabe trader joe's

so we've been trying to find a snack which tastes like the aussie one twisties

And this is the one that everyone said try

and we never found.

So a listener found it for us and brought it to a talk I was doing in North Carolina.

Do you want to open it?

Num nom nom nom num.

That's how it works.

They're good.

That's good.

They're really good.

That's good.

Now I want to try them versus the

Wenzels.

No, won't we?

The texture is there.

The flavour is a little hollow.

It's a little too subtle.

Twisties really punch you in the face.

But they're good.

Look, the texture is spot on.

Thank you very much.

To the listener, do you have anything?

Thank you.

No,

I forgot your names.

You were wonderful people.

Thank you for these.

Tell us who you are.

Yes.